Point Convergence Analysis of the Accelerated Gradient Method for Multiobjective Optimization: Continuous and Discrete
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909900245827584 |
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| author | Yin, Yingdong |
| author_facet | Yin, Yingdong |
| contents | This paper investigates the point convergence of accelerated gradient methods for multiobjective optimization, in both continuous and discrete settings. We address the open problems of whether the solution trajectory of the multiobjective inertial gradient-like dynamical system (MAVD) with asymptotic vanishing damping converges when $α= 3$, and whether the sequence generated by the multiobjective Nesterov accelerated method (MAG) converges to a weakly Pareto optimal solution. For the continuous system (MAVD) with $α= 3$, we prove that the trajectory $x(t)$ converges to a weakly Pareto optimal solution. For the discrete case, we propose a multiobjective accelerated gradient method with a generalized momentum factor (MAG-GM), and prove that the generated sequence $\{x_k\}$ converges to a weakly Pareto optimal solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26382 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Point Convergence Analysis of the Accelerated Gradient Method for Multiobjective Optimization: Continuous and Discrete Yin, Yingdong Optimization and Control This paper investigates the point convergence of accelerated gradient methods for multiobjective optimization, in both continuous and discrete settings. We address the open problems of whether the solution trajectory of the multiobjective inertial gradient-like dynamical system (MAVD) with asymptotic vanishing damping converges when $α= 3$, and whether the sequence generated by the multiobjective Nesterov accelerated method (MAG) converges to a weakly Pareto optimal solution. For the continuous system (MAVD) with $α= 3$, we prove that the trajectory $x(t)$ converges to a weakly Pareto optimal solution. For the discrete case, we propose a multiobjective accelerated gradient method with a generalized momentum factor (MAG-GM), and prove that the generated sequence $\{x_k\}$ converges to a weakly Pareto optimal solution. |
| title | Point Convergence Analysis of the Accelerated Gradient Method for Multiobjective Optimization: Continuous and Discrete |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2510.26382 |